A113545 Numbers both pentagon-free and squarefree.

1, 2, 3, 6, 7, 11, 13, 14, 17, 19, 21, 23, 26, 29, 31, 33, 34, 37, 38, 39, 41, 42, 43, 46, 47, 53, 57, 58, 59, 61, 62, 67, 69, 71, 73, 74, 77, 78, 79, 82, 83, 86, 87, 89, 91, 93, 94, 97, 101, 103, 106, 107, 109, 111, 113, 114, 118, 119, 122, 123, 127, 129

Offset: 1

Author

Jonathan Vos Post, Jan 13 2006

Keywords

• easy
• nonn

References

• Bellman, R. and Shapiro, H. N. "The Distribution of Squarefree Integers in Small Intervals." Duke Math. J. 21, 629-637, 1954.
• Borwein, J. and Bailey, D. Mathematics by Experiment: Plausible Reasoning in the 21st Century. Natick, MA: A. K. Peters, 2003.
• Hardy, G. H. and Wright, E. M., Section 18.6 in An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, pp. 269-270, 1979.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Squarefree.

Crossrefs

Cf. A000217, A005117, A113502, A013929, A046098, A059956, A065474, A071172, A087618, A088454, A112886, A113508.

Programs

Mathematica

bad = Rest@Union[Range[14]^2, # (3 # - 1)/2 &@ Range[11]]; Select[ Range[200], {} == Intersection[ bad, Divisors[#]] &] (* Giovanni Resta, Jun 13 2016 *)

Formula

a(n) has no factor >1 of form b^2 nor c*(3*c-1)/2. A005117 INTERSECTION A113508.

Extensions

Data corrected by Giovanni Resta, Jun 13 2016